93ed6: Difference between revisions
→Theory: copypasty from 101ed7 |
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93ed6 is nearly identical to [[36edo]], but with the 6th harmonic rather than the [[2/1|octave]] being just. The octave is stretched by about 0.757 [[cent]]s (almost identical to [[101ed7]], where the octave is stretched by about 0.770 cents). Like 36edo, 93ed6 is [[consistent]] to the [[integer limit|8-integer-limit]]. | 93ed6 is nearly identical to [[36edo]], but with the 6th harmonic rather than the [[2/1|octave]] being just. The octave is stretched by about 0.757 [[cent]]s (almost identical to [[101ed7]], where the octave is stretched by about 0.770 cents). Like 36edo, 93ed6 is [[consistent]] to the [[integer limit|8-integer-limit]]. | ||
Compared to 36edo, 93ed6 is pretty well optimized for the 2.3.7.13.17 [[subgroup]], with slightly better [[3/1|3]], [[7/1|7]], [[13/1|13]] and [[17/1|17]], and a slightly worse 2 versus 36edo. Using the [[patent val]], the [[5/1|5]] is also less accurate. Overall this means 36edo is still better in the [[5-limit]], but 93ed6 is better in the [[13-limit|13-]] and [[17-limit]], especially when treating it as a dual-5 dual-11 tuning. | Compared to 36edo, 93ed6 is pretty well optimized for the 2.3.7.13.17 [[subgroup]], with slightly better [[3/1|3]], [[7/1|7]], [[13/1|13]] and [[17/1|17]], and a slightly worse 2 versus 36edo. Using the [[patent val]], the [[5/1|5]] is also less accurate. Overall this means 36edo is still better in the [[5-limit]], but 93ed6 is better in the [[13-limit|13-]] and [[17-limit]], especially when treating it as a dual-5 dual-11 tuning. | ||
The local [[The Riemann zeta function and tuning #Optimal octave stretch|zeta peak]] around 36 is located at 35.982388, which has a step size of 33.3496{{c}} and has octaves stretched by 0.587{{c}}, making 93ed6 very close to optimal for 36edo. | |||
=== Harmonics === | === Harmonics === | ||